Problem 9: A body of mass m drops from bridge into water of the river. The bridge is 10 m high from the water surface.

(a) Find the speed of the body 5 m above the water surface.

(b) Find the speed of the body before it strikes the water.

Solution

Theory: When the mass is on the surface of the bridge, it has some P.E relative to the surface of water and the distance down. This P.E converts to K.E as the object falls. At any instant of time, its K.E is equal to the loss in the P.E. So, we calculate the K.E 5 m below the surface of the bridge and then find the velocity at that point. Then we find loss in P.E before striking the water surface (10 m) which is the K.E of the object at that point and find the velocity.

• P.E at the surface of bridge = mgh = m× 9.8 × 10 = 98m jouls

P.E when it falls 5 meter = m × 9.8 × 5 = 49m jouls

Difference in P.E = K.E = 98m – 49m = 49m jouls. Therefore,

½ mv2 = 49m        OR       v2 = 2 × 49 = 98        OR       v = √98 = 9.899 = 9.9 ms-1

Therefore, velocity of the body 5 m above the water surface is 9.9 ms-1.

• For the second part, P.E at the surface of water = 0

Therefore, loss in P.E = Gain in K.E         OR         K.E = 98m      OR       ½ mv2 = 98m

OR   v2 = 2 × 98 = 196           OR           v = √196 = 14 ms-1

Therefore, velocity of the body when it just strikes the surface of water .